Lecture 13 : Solution thermodynamics - Part II

[Music] [Music] solution thermodynamics concept standard at a stand at any temperature free energy g at the temperature system at one atmosphere standard State value free energyy entropy K enpy or absolute value stand fraction ideal gas mixture consider gas miid binary system phe equ gas ideal gas mixture Pham par already mixing of gas Delta p t composition composition pressure composition temperature constant a Val bi partial partial molar volume of I component in the mixture okay State function set a function of pressure temperature and ni prime prime total volume okay V Prime equal to d n i p t other components constant a Val nothing but this partial partial molar volume partial B volume of the component I component V Prime P which is total pressure equal to summation of Ni when total number of moles in the mixture RT by this one I can write since gases are ideal the V Prime equal to P partial differentiation Cy should be equal to RT by P a constant RT by P VI Prime is nothing but RT by P equal to P nothing but summation of n RT by V Prime summation of B Prime partial mol volume of I component it nothing but total volume by summation of all the moles present in the mixture okay Journey for ideal system Pi partial pressure of I component equal to n r t by V Prime class lecture 12 V Prime equal to na a RT by Pi partial pressure of I component in the system partial M volume vi v Prime by summ of n equal to na RT by summation of n into pi x RT by pi a equation P molar partial volume of aat component equal to XI mole fraction of IOD component in the gas mixture by partial pressure of IOD component equation p i bar Delta g i bar equal to xiir T Pi into this one I will get GI bar which is nothing but chemical potential of I component to stage two equal to total pressure relation P equal to x i p would be equal to x i DP that means DP would be equal to DPI XI would be equal to G2 GI minus would be equal to RT Ln pi 2 pi1 fine okay partial pressure of component P let's say I consider p i partial pressure of compon one atmosphere at any temperature any temperature Ln pi state two should be equal to zero toon GI 2 not two this is one stage one it gi1 would be equal to Z not ini at that means gas Vol free energy difference initial reference G not for that particular gas okay GI chemical potential of I component partial molar free energy for I component in the mixture would be equal to G Plus RT Ln Pi okay if have that of IOD component equal to GI not Plus RT Ln Pi Pi equal to x i total pressure it be equal to plus RT Ln x i plus RT Ln p f it into chemical potential of I equal to standard chemical potential plus RT Ln XI plus RT Ln p okay okay number gas mix okay mix okay gal to H minus TS say equation Delta G delta T P equal to minus s equation Delta gal V DP minus sdt equ gal to H minus plus T to find out DH mix of ideal gas mixtures of ideal gas mixture composition F comp pressure FY condition DH mix of ideal gas mixture composition fix pressure fix Cate expand c equal to plus T Delta G temperature T Delta G minus G Delta delt = t² equal to minus H DT t² d y DX minus X Dy y s x g or y t d g by T should be equal to this one Thom D G by t equal to minus H DT t² okay okay D Delta G by T we can write Delta H delta T t² we can also write that our CL system pressure constant okay would be equal to plus RT Ln x i + RT Ln p would be equal to DT Plus x i plus Ln p partial differentiation with respect to temperature is not dependent on temperature condition imp composition fix that means XI fix pressure fix that means pressure fix due to a constant R is a constant term universal gas constant g i partial molar free energy of I component by T is equal to D this should be partial molar enthalpy of a component divided by t² with a minus sign similarly not this this one combine minus standard enthalpy of component when it is p at one atmosphere pressure t² t sare h i bar equal to h i that means before mixing enthalpy I standard value for pure is equal to after mixing partial molar enalia of I component in the M for that particular Pi for that particular component equal difference calate DH mix for component press composition fix minus this final minus initial after mixing H after mixing minus H before mixing 4 I is equal to 0 okay consideration for ideal solution ideal mixing mixing homogeneous homogeneous mixing dels DH mix equal to zero our n heat content interaction of mixing Z physically physically no interaction between molecules of the atoms it gas gals consider enthalpy of mixing of those molecules or those in this case it will be atoms atoms enpy of mixing enpy of mixing zero aluminium iron nickel titanium element at system iron phosphorus phosphorus positive interaction negative interaction different human human behavi negative interaction human zh mix negative mix of mixing zero interaction mixing free energy deter at the same time mixing entropy Det [Music] [Music] [Music]